KNOT TYPES OF SATELLITE KNOTS AND TWISTED KNOTS
KNOT TYPES OF SATELLITE KNOTS AND TWISTED KNOTS
复制标题
卫星结和捻结的结类型
DOI：
10.1142/9789812796097_0004
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发表时间：
2008
影响因子：
0.8
通讯作者：
Kimihiko Motegi
中科院分区：
文献类型：
--
作者：
Kimihiko Motegi
设K是三维球面S3中一个标准嵌入的实心环面V内的纽结。在下文中，对于非平凡性，我们假设K不能位于V中的3-球中。将实心环面V以另一个纽结的形状打结，如图0.1所示，作为K的图像，我们得到S3中的新纽结K'。以这种方式获得的结称为卫星结。另一方面，将实心环面V扭曲几次，我们在S3中得到一个新的纽结K”。本文的目的是对这类构式的研究作一综述。
Let K be a knot inside a standardly embedded solid torus V in the 3-sphere S3. In the following , for nontriviality , we assume that K cannot be lie in a 3-ball in V. Knotting the solid torus V in the shape of another knot as in Figure 0.1, as the image of K, we obtain a new knot K' in S3. A knot obtained in such a manner is called a satellite knot . On the other hand, twisting the solid torus V several times, we get a new knot K" in S3. The purpose in this article is to give a survey of some aspects of the study of these constructions.